Green-schwarz Iib Superstring The Nambu-goto Action Of The K-symmetry And Related Issues

The method of quantum field theory is used in condensed matter physics extensively. Some improtant mechanisms in condensed matter physics is related with soliton and scattering amplitude et cetera in field theory. These year, more and more physicist have payed their attention to the intrinsic relations between condensed matter physics and string theory which is the frontier of field theory.The reseach area of the applicant's master thesis include the κ-symmetry of Green-Schwarz superstring actions and their parametrization of supergoup.κ-symmetry is local supersymmetry of Green-Schwarz superstring action: the action is invariant with respect to the local κ-transformations. The local κ-transformations of metric and field variables are given for the action of Polyakov form customarily. A disadvantage to this formulation of κ-transformations is that it includes metric variation. This cause ambiguity in both off shell and on shell cases. However, the action of type IIB superstring in AdS₅ ⊕ S⁵ background given by R.R.Metsaev and A.A.Tseytlin(MT) can be reformulated in the Nambu-Goto(NG) form. For this form we give the new projection operator involving vielbeins in the target space to construct local κ-transformations which leaves the NG form action invariant. This new formulation of κ-symmetry(called target space form)is first suggested by Schwarz for Green-Schwarz(GS) model. Since the difference between GS model and MT model, our construction has some new aspects, which is applicable for all models similar to MT model. An example is given for AdS₅ ⊕ S⁵ IIB superstring. We also study κ-symmetry in target space form for Polyakov model.The action and equations of motion of superstring propagating in some AdS background is formulated by current J = G^-1dG generally. Whereas the current should satisfy Maurer-Carton equations dJ + J∧J = 0 implied by the structure of the superal-gebra. These Carton 1-forms are not independent variables. We must parametrize the supergoup because the action should be expressed by independent mechanical variables when quantizing superstring and solving its equations of motion.. Two formulation ofparameterization of the supergroup 51/(2,2|4) are analyzed respectively. They are G = e*iP*H*iiJii+<>""''QL> and G = e9'°n'QL-e*"p*. Commutation relations for the generators of superalgebra su(2.2|4) are used to achieve the expression of the current, We find that different parameterizations give different expressions of the current. It shows that the current is in the form of exponential expression of an adjoint matrix. Kallosh et.al gave a method of parametrizing the supergroup of superstring in AdS$ ? S5 background by gauge fix the local /t-symmetry. The superconformal actions can be simplified dramatically. But their treatment is too complicated and difficult to be extended to other models. We propose a new simplier method of parametrization which is based upon their idea. Take the case of Polyakov model, the simplified 1-forms are given.